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Simplifying 1242.0584 = 2(3.14r2) + 2 * 3.14r * 38.3 Remove parenthesis around (3.14r2) 1242.0584 = 2 * 3.14r2 + 2 * 3.14r * 38.3 Multiply 2 * 3.14 1242.0584 = 6.28r2 + 2 * 3.14r * 38.3 Reorder the terms for easier multiplication: 1242.0584 = 6.28r2 + 2 * 3.14 * 38.3r Multiply 2 * 3.14 1242.0584 = 6.28r2 + 6.28 * 38.3r Multiply 6.28 * 38.3 1242.0584 = 6.28r2 + 240.524r Reorder the terms: 1242.0584 = 240.524r + 6.28r2 Solving 1242.0584 = 240.524r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1242.0584 + -240.524r + -6.28r2 = 240.524r + -240.524r + 6.28r2 + -6.28r2 Combine like terms: 240.524r + -240.524r = 0.000 1242.0584 + -240.524r + -6.28r2 = 0.000 + 6.28r2 + -6.28r2 1242.0584 + -240.524r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1242.0584 + -240.524r + -6.28r2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -197.78 + 38.3r + r2 = 0 Move the constant term to the right: Add '197.78' to each side of the equation. -197.78 + 38.3r + 197.78 + r2 = 0 + 197.78 Reorder the terms: -197.78 + 197.78 + 38.3r + r2 = 0 + 197.78 Combine like terms: -197.78 + 197.78 = 0.00 0.00 + 38.3r + r2 = 0 + 197.78 38.3r + r2 = 0 + 197.78 Combine like terms: 0 + 197.78 = 197.78 38.3r + r2 = 197.78 The r term is 38.3r. Take half its coefficient (19.15). Square it (366.7225) and add it to both sides. Add '366.7225' to each side of the equation. 38.3r + 366.7225 + r2 = 197.78 + 366.7225 Reorder the terms: 366.7225 + 38.3r + r2 = 197.78 + 366.7225 Combine like terms: 197.78 + 366.7225 = 564.5025 366.7225 + 38.3r + r2 = 564.5025 Factor a perfect square on the left side: (r + 19.15)(r + 19.15) = 564.5025 Calculate the square root of the right side: 23.759261352 Break this problem into two subproblems by setting (r + 19.15) equal to 23.759261352 and -23.759261352.Subproblem 1
r + 19.15 = 23.759261352 Simplifying r + 19.15 = 23.759261352 Reorder the terms: 19.15 + r = 23.759261352 Solving 19.15 + r = 23.759261352 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-19.15' to each side of the equation. 19.15 + -19.15 + r = 23.759261352 + -19.15 Combine like terms: 19.15 + -19.15 = 0.00 0.00 + r = 23.759261352 + -19.15 r = 23.759261352 + -19.15 Combine like terms: 23.759261352 + -19.15 = 4.609261352 r = 4.609261352 Simplifying r = 4.609261352Subproblem 2
r + 19.15 = -23.759261352 Simplifying r + 19.15 = -23.759261352 Reorder the terms: 19.15 + r = -23.759261352 Solving 19.15 + r = -23.759261352 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-19.15' to each side of the equation. 19.15 + -19.15 + r = -23.759261352 + -19.15 Combine like terms: 19.15 + -19.15 = 0.00 0.00 + r = -23.759261352 + -19.15 r = -23.759261352 + -19.15 Combine like terms: -23.759261352 + -19.15 = -42.909261352 r = -42.909261352 Simplifying r = -42.909261352Solution
The solution to the problem is based on the solutions from the subproblems. r = {4.609261352, -42.909261352}
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